1. Field of the Invention
This invention relates generally to the art of mathematics instruction and, more particularly, is related to an apparatus and associated technique for visually conveying to students the processes involved in mathematics, particularly with respect to subtraction.
2. Description of the Prior Art
Various methods and apparatuses have been heretofore proposed for use as visual teaching aids in mathematics. Many of such devices have relied on the principles of the ancient abacus, a counting frame with rows of beads sliding on wires. Such devices have taken numerous forms in the past, but all have as a common objective the provision of a visual teaching aid and method which simplifies, insofar as possible, the basic concepts of and principles of operation involved in mathematics. Prior United States patents in this art of which I am aware include the following U.S. Pat. Nos. 1,826,034; 2,369,804; 2,866,278; and 3,129,518.
Each of the devices described in the foregoing patents suffers from one or more deficiencies. In my view, the proliferation of prior art attempts to devise a simplified visual teaching aid attests to the fact that there still exists a tremendous need to simplify and clarify such apparatuses and associated instructional techniques until everything possible has been done to meet the needs of the slow-learning child having limited abilities, such as a retarded child. While many prior art devices have attempted to expand or generalize an overall understanding of arithmetic, such expansion and generalization, I have found, often obscures the necessary and basic concepts involved in, for example, subtraction, to the slow-learning or retarded child. Given the fact that the communication of mathematical concepts is most difficult with a slow-learning or retarded child, it follows that the greatest need exists for a device which can be utilized as a visual mathematical teaching aid when dealing with such disadvantaged children or slow-learning students.
Another deficiency inherent in the prior art devices is their limited ability to appeal only to a child's visual learning sense. While several prior art devices do appear to utilize manual manipulation of beads, logs, or the like, the mathematical values represented by such workpieces must be re-translated into numerical components to complete the learning process. The additional step of translating representative workpieces into associated component values is, I have found, a substantial inhibiting factor in the learning processes involved with a retarded or otherwise slow-learning student. It is therefore understood that an apparatus and method which can, by and large, eliminate this intermediate step would be of great value.
The teaching aid device and technique advanced in my earlier patent application identified above goes a long way towards solving many of the above-stated problems with respect to prior art devices. More particularly, my invention described and claimed in the earlier application comprises a support member having a surface divided into a plurality of work areas arranged in a column and row form. There is provided one column corresponding to each place-value component, i.e., ones, tens, hundreds, thousands, ten thousands, etc. The work areas, which preferably comprise receptacles for workpieces, are arranged in increasing widths from right to left. A plurality of sets of workpieces are also provided, the number of sets corresponding to the number of columns of place-value components. The workpieces within each set have a three-dimensional physical configuration corresponding to one of the place-value components. The width of the workpieces of each set correspond to the width of its corresponding column such that each column may accommodate only those workpieces having the appropriate place value. At least two rows of work areas or compartments are defined for each column, one row having an area for accommodating no more than nine workpieces, the other row having an area for accommodating no more than ten workpieces. The latter row is extremely useful in the subtraction process for illustrating re-grouping of a higher order place-value component to its ten lower order components.
While the structure described in my earlier application is particularly useful in aiding the teaching process with respect to slow-learning students, I have found that the more intelligent young children, who need to be taught the same basic processes, are somewhat frustrated by the inherent slow speed with which that apparatus must be manually manipulated. In other words, while uniquely suited for slow-learners, I have found a need to automate somewhat the basic apparatus described in my earlier application in order to attract the quicker learning child of normal intelligence. It is towards this end that the instant application is advanced.